Question

Solve 3x+1 = 15 for x using the change of base formula log, y=
log y
b log b
0-0.594316
O 1.405684
O 1.469743
O 3.469743

Answer 1

Solved given expression for x using the change of base formula log base b of y equals log y over log b is 1.46497

Step-by-step explanation:

Given Expression:

             $3^{x+1}=15$

To solve this, first convert the exponential form into log form

If $a^{x}=b \text { then } \log _{a} b=x$

So, when comparing the given expression with above,  a = 3, x = x + 1 and b = 15.

$3^{x+1}=15$ become as $x+1=\log _{3}(15)$

Now, apply change of base formula to remove base 3 ,

       $\log _{a}(y)=\frac{\log y}{\log a}$

Hence,

     $\log _{3}(15)=\frac{\log 15}{\log 3}$

Substitute $x+1=\log _{3}(15)$ in above expression, we get

     $x+1=\frac{\log 15}{\log 3}$

    $x+1=\frac{1.17609}{0.47712}$

    x + 1 = 2.46497

    x = 2.46497 - 1

    x = 1.46497